Showing papers on "Stefan number published in 2019"

Solar Still Efficiency Enhancement by Using Graphene Oxide/Paraffin Nano-PCM

Abstract: Solar-driven water desalination technologies are rapidly developing with various links to other renewable sources. However, the efficiency of such systems severely depends on the design parameters. The present study focused on using graphene oxide (GO) with the Φ = 0.2, 0.4 and 0.6 wt.% dispersed in paraffin, as phase-change materials (PCMs), to improve the productivity of a solar still for desalination applications. The outcomes showed that by adding more graphene oxide to paraffin, the melting temperature got reduced. Solar still with GO/paraffin showed 25% productivity improvement in comparison with the solar still with only PCM. The obtained Nusselt number during the melting time also represented that free convection heat transfer into the melted region of the solar still has been enhanced by adding dispersed GO to the PCM, compared to the base paraffin. Also, increasing the hot wall temperature augments the Nusselt number. Finally, an empirical equation was derived to correlate the average Nusselt number as a function of Rayleigh number (Ra), the Stefan number (Ste), the subcooling factor (Sb), and the Fourier number (Fo). The obtained correlation depicted that Nusselt number enhancement has a reverse relation with Fourier number.

Nano-enhancement of phase change material in a shell and multi-PCM-tube heat exchanger

Abstract: The fundamental defect of PCMs in discharging process is their low conductivity which results in long solidification time. In this study distribution of a PCM in a multi-tube heat exchanger is conducted numerically to reduce the solidification time. Therefore, the PCM mass is distributed in the inner and outer tubes between which a heat transfer fluid (HTF) passes through. Various volume fractions of copper nanoparticles are added to the PCM and the consequences of the conductivity enhancement is observed. Moreover, the variation of Stefan number (Ste) is considered to evaluate the effect of this parameter on the solidification process. In addition, it is shown that the distribution of the PCM is greatly effective on the heat transfer enhancement. Proper PCM mass distribution leads to 62% reduction in the solidification time. Results also indicates that by increasing the nanoparticles volume fractions to 4% and Ste to 0.45, the solidification time reduces 15% and 26%, respectively in the best case.

Efficient lattice Boltzmann method for electrohydrodynamic solid-liquid phase change.

Abstract: Melting in the presence of electrohydrodynamic (EHD) flow driven by the Coulomb force in dielectric phase change material is numerically studied. A model is developed for the EHD flow in the solid-liquid phase change process. The fully coupled equations including mechanical equations, electrical equations, energy equations, and the continuity equations in the solid-liquid interface are solved using a unified lattice Boltzmann model (LBM). Firstly, the numerical model is validated by several cases in the hydrostatic state, and all LBM results are found to be highly consistent with analytical solutions. Besides, our LBM code is able to reproduce the step changes in the distribution of charge density and electric field due to the discontinuous distribution of physical properties at the interface. Then, a systematical investigation is conducted on various nondimensional parameters, including electric Rayleigh number T, Prandtl number Pr, and Stefan number St. Results are presented for the transient evolutions of temperature, fluid flow, charge density fields, and liquid fraction. Four flow stages in the melting process together with three kinds of flow instabilities are observed. It is found that the electric field has significant influence on the melting, especially at high T and Pr and low St. Over the tested cases, a maximum melting time saving of around 50% is found.

Numerical and experimental investigation of paraffin wax melting in spherical cavity

Abstract: Various process parameters influence the melting and solidification phase change process. Studies on the influence of shape of cavity, thermo-physical properties of the phase change material and the boundary conditions, on the phase change process, has been carried out by various researchers worldwide. The effect of the thermal properties of the cavity material on the process is yet to be investigated thoroughly. In this work, melting process of paraffin wax is simulated in a spherical cavity for various cavity materials having different thermal properties and for different boundary conditions. The simulations results are obtained using enthalpy-porosity model for free surface melting process, solved using Ansys-fluent 16.2. Experimental studies were carried out for one type of cavity material. The experimental investigation included visualization of shape of solid fraction which is used to validate the numerical approach of this computational study. The results showed that the materials having higher thermal diffusivity has enhanced melting rate because of increased bouncy effect and convection. It has been found that the higher Stefan number shows the effect of higher natural convection and maximum velocity profile, resulting in enhanced melting process. These simulations are significant for selection of cavity material for different processes like energy storage, melting-solidification of metal in casting and others.

Comparison of the quasi-steady-state heat transport in phase-change and classical Rayleigh-Bénard convection for a wide range of Stefan number and Rayleigh number

Abstract: We report the first comparative study of the phase-change Rayleigh–Benard (RB) convection system and the classical RB convection system to systematically characterize the effect of the oscillating solid-liquid interface on the RB convection. Here, the role of Stefan number Ste (defined as the ratio between the sensible heat to the latent heat) and the Rayleigh number based on the averaged liquid height Raf is systematically explored with direct numerical simulations for low Prandtl number fluid (Pr = 0.0216) in a phase-change RB convection system during the stationary state. The control parameters Raf (3.96 × 104 ≤ Raf ≤ 9.26 × 107) and Ste (1.1 × 10−2 ≤ Ste ≤ 1.1 × 102) are varied over a wide range to understand its influence on the heat transport and flow features. Here, we report the comparison of large-scale motions and temperature fields, frequency power spectra for vertical velocity, and a scaling law for the time-averaged Nusselt number at the hot plate Nuh¯ vs Raf for both the RB systems. The intensity of solid-liquid interface oscillations and the standard deviation of Nuh increase with the increase in Ste and Raf. There are two distinct RB flow configurations at low Raf independent of Ste. At low and moderate Raf, the ratio of the Nusselt number for phase-change RB convection to the Nusselt number for classical RB convection Nuh¯/NuhRB¯ is always greater than one. However, at higher Raf, the RB convection is turbulent, and Nuh¯/NuhRB¯ can be less than or greater than one depending on the value of Ste. The results may turn out to be of immense consequence for understanding and altering the transport characteristics in the phase-change RB convection systems.

Numerical investigation of paraffin wax solidification in spherical and rectangular cavity

Abstract: The solid-liquid phase change processes are very sensitive to thermal boundary conditions. The phase change processes are also dominated by the shape of the cavity and thermo-physical properties of phase change materials. The transient experimental studies of unconstrained phase change processes are very difficult. Therefore, the numerical simulation is chosen to study the solidification phase change process in a rectangular and a spherical cavity. In this work, the solidification process of paraffin wax is simulated in a spherical cavity and a rectangular cavity for different thermal boundary conditions. The different sizes of cavities are taken to show the impact of shape on the solidification process. The simulations results are obtained using enthalpy-porosity model for free surface solidification process. The commercial software Ansys-fluent 16.2 is used to solve the numerical model. The model used for simulation is validated in previous work for melting in a spherical cavity [1] The result shows the solidification time is minimum for highest Stefan number. It also reveals that the solidification process is slow as the thickness of the solid zone increases. This is because of decreasing effect of natural convection and increasing effect of conductive resistance of solidified phase change material. The conduction dominated process makes the solidification slower as the thermal conductivity of paraffin wax is low. Different shapes of cavity, effects the solidification time. This research shows that though the size of spherical cavity is higher than that of rectangular cavity, the solidification time is much lower for spherical cavity.

Fluctuation-dissipation analysis of nonequilibrium thermal transport at the hydrate dissociation interface.

Abstract: Herein, a nonequilibrium molecular-dynamics simulation in an NVE ensemble was performed to investigate the spontaneous dissociation of methane-hydrate when it came in contact with liquid water. The nonequilibrium in the interface region is linked to the dissociation process of the hydrate near the interface according to the Onsager's hypothesis. The simulated thickness of the interface was found to be close to the acoustic phonon mean path of methane hydrate and agreed with the reference value. The normalized heat flow autocorrelation function was introduced to study fluctuation–dissipation in terms of the thickness and moving velocity of the interface and the Stefan number. This helped to clearly identify three distinct hydrate-decomposition regimes dominated by sensible heat, latent heat and an intrinsically unstable lattice framework. It was found that the fluctuation–dissipation theory could express the nonequilibrium nature in the front two stages before the threshold was reached, and the dissociation rate increased in the latter stage; this was different from the case of thermal-driven dissociation. The Stefan number decreased rapidly with dissociation in the initial stage and then fluctuated in the intermediate stage; this was analogous to the fluctuation characteristics of the heat flow autocorrelation function. The Stefan number effect shows that thermal dissipation drives the hydrate dissociation and correlates fluctuation to the nonequilibrium nature. It was also found that a small Stefan number was enough to break up the residual hydrate soon after the threshold was achieved. The transient interfacial thermal resistance of the interfacial region was obtained as a typical value in the range of 10−7–10−9 m2 K W−1. This justifies that fluctuation–dissipation exists in the nonequilibrium process of hydrate dissociation either in terms of heat flux, as observed in this study, or the diffusion of guest molecules, as reported in other studies.

The Stefan problem with variable thermophysical properties and phase change temperature

Abstract: In this paper we formulate a Stefan problem appropriate when the thermophysical properties are distinct in each phase and the phase-change temperature is size or velocity dependent. Thermophysical properties invariably take different values in different material phases but this is often ignored for mathematical simplicity. Size and velocity dependent phase change temperatures are often found at very short length scales, such as nanoparticle melting or dendrite formation; velocity dependence occurs in the solidification of supercooled melts. To illustrate the method we show how the governing equations may be applied to a standard one-dimensional problem and also the melting of a spherically symmetric nanoparticle. Errors which have propagated through the literature are highlighted. By writing the system in non-dimensional form we are able to study the large Stefan number formulation and an energy-conserving one-phase reduction. The results from the various simplifications and assumptions are compared with those from a finite difference numerical scheme. Finally, we briefly discuss the failure of Fourier's law at very small length and time-scales and provide an alternative formulation which takes into account the finite time of travel of heat carriers (phonons) and the mean free distance between collisions.

Mapping a regime diagram for the slurry F-layer at the base of Earth’s outer core

Abstract: Seismic observations of a slowdown in P wave velocity at the base of Earth's outer core suggest the presence of a stably-stratified region known as the F-layer. This raises an important question: how can light elements that drive the geodynamo pass through the stably-stratified layer without disturbing it? We consider the F-layer as a slurry containing solid particles dispersed within the liquid iron alloy that snow under gravity towards the inner core. We present a regime diagram showing how the dynamics of the slurry F-layer change upon varying the key parameters: Peclet number (Pe), the ratio between advection and chemical diffusion; Stefan number (St), the ratio between sensible and latent heat; and Lewis number (Le), the ratio between thermal and chemical diffusivity. We obtain four regimes corresponding to stable, partially stable, unstable and no slurries. No slurry is found when the heat flow at the base of the layer exceeds the heat flow at the top, while a stably-stratified slurry arises when advection overcomes thermal diffusion (Pe≳Le) that exists over a wide range of parameters relevant to the Earth's core. Our results estimate that a stably-stratified F-layer gives a maximum inner-core boundary (ICB) body wave density jump of Δρbod≤534kgm−3 which is compatible with the lower end of the seismic observations where 280≤Δρbod≤1,100kgm−3 is reported in the literature. With high thermal conductivity the model predicts an inner core age between 0.6 and 1.2Ga, which is consistent with other core evolution models. Our results suggest that a slurry model with high core conductivity predicts geophysical properties of the F-layer and core that are consistent with independent seismic and geodynamic calculations.

Integral Solution of Two-Region Solid–Liquid Phase Change in Annular Geometries and Application to Phase Change Materials–Air Heat Exchangers

Abstract: A mathematical model based on the integral method is developed to solve the problem of conduction-controlled solid–liquid phase change in annular geometries with temperature gradients in both phases. The inner and outer boundaries of the annulus were subject to convective, constant temperature or adiabatic boundary conditions. The developed model was validated by comparison with control volume-based computational results using the temperature-transforming phase change model, and an excellent agreement was achieved. The model was used to conduct parametric studies on the effect of annuli geometry, thermophysical properties of the phase change materials (PCM), and thermal boundary conditions on the dynamics of phase change. For an initially liquid PCM, it was found that increasing the radii ratio increased the total solidification time. Also, increasing the Biot number at the cooled (heated) boundary and Stefan number of the solid (liquid) PCM, decreased (increased) the solidification time and resulted in a greater (smaller) solid volume fraction at steady state. The application of the developed method was demonstrated by design and analysis of a PCM–air heat exchanger for HVAC systems. The model can also be easily employed for design and optimization of annular PCM systems for all associated applications in a fraction of time needed for computational simulations.

Approximate solutions to the one-phase Stefan problem with non-linear temperature-dependent thermal conductivity

Abstract: In this chapter we consider different approximations for the one-dimensional one-phase Stefan problem corresponding to the fusion process of a semi-infinite material with a temperature boundary condition at the fixed face and non-linear temperature-dependent thermal conductivity. The knowledge of the exact solution of this problem, allows to compare it directly with the approximate solutions obtained by applying the heat balance integral method, an alternative form to it and the refined balance integral method, assuming a quadratic temperature profile in space. In all cases, the analysis is carried out in a dimensionless way by the Stefan number (Ste) parameter.

Thermal Characterization of a Heat Management Module Containing Microencapsulated Phase Change Material

Abstract: In this study, a heat management module containing a microencapsulated phase change material (mPCM) was fabricated from mPCM (core material: paraffin; melting temperature: 37 °C) and aluminum honeycomb structures (8 mm core cell). The aluminum honeycomb functioned both as structural support and as a heat transfer channel. The thermal management performance of the proposed module under constant-temperature boundary conditions was investigated experimentally. The thermal protection period of the module decreased as the Stefan number increased; however, increasing the subcooling factor could effectively enhance the thermal protection performance. When the cold-wall temperature TC was fixed at 17 °C and the initial hot wall temperature was 47–67 °C, the heat dissipation of the module was complete 140 min after the hot-wall heat supply was stopped. The time required to complete the heat dissipation increased to 280 min when TC increased to 27 °C.

A Non-local Formulation of the One-Phase Stefan Problem Based on Extended Irreversible Thermodynamics

Abstract: Non-local effects are introduced into a mathematical description of a solidification process based on Fourier’s law with a size-dependent thermal conductivity. An asymptotic solution based on a large Stefan number is proposed. The agreement with the numerical solution is excellent for any Nusselt number.

Quantitative analysis on influencing factors for interface propagation-based thermal conductivity measurement method during solid-liquid transition

Abstract: The recently proposed interface propagation-based method has shown its advantages in obtaining the thermal conductivity of phase change materials during solid-liquid transition over conventional techniques. However, in previous investigation, the analysis on the measurement error was qualitative and only focused on the total effects on the measurement without decoupling the influencing factors. This paper discusses the effects of influencing factors on the measurement results for the interface propagation-based method. Numerical simulations were performed to explore the influencing factors, namely model simplification, subcooling and natural convection, along with their impact on the measurement process and corresponding measurement results. The numerical solutions were provided in terms of moving curves of the solid-liquid interface and the predicted values of thermal conductivity. Results indicated that the impact of simplified model was strongly dependent on Stefan number of the melting process. The degree of subcooling would lead to underestimated values for thermal conductivity prediction. The natural convection would intensify the heat transfer rate in the liquid region, thereby overestimating the obtained results of thermal conductivity. Correlations and experimental guidelines are provided. The relative errors are limited in ±1.5%, ±3%and ±2% corresponding to the impact of simplified model, subcooling and natural convection, respectively.